Sekihara / Nagarajan Adaptive Spatial Filters for Electromagnetic Brain Imaging

1. Auflage 2008
ISBN: 978-3-540-79370-0
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 245 Seiten

Reihe: Engineering (R0)

Neural activity in the human brain generates coherent synaptic and intracellular currents in cortical columns that create electromagnetic signals which can be measured outside the head using magnetoencephalography (MEG) and electroencephalography (EEG). Electromagnetic brain imaging refers to techniques that reconstruct neural activity from MEG and EEG signals. Electromagnetic brain imaging is unique among functional imaging techniques for its ability to provide spatio-temporal brain activation profiles that reflect not only where the activity occurs in the brain but also when this activity occurs in relation to external and internal cognitive events, as well as to activity in other brain regions. Adaptive spatial filters are powerful algorithms for electromagnetic brain imaging that enable high-fidelity reconstruction of neuronal activity. This book describes the technical advances of adaptive spatial filters for electromagnetic brain imaging by integrating and synthesizing available information and describes various factors that affect its performance. The intended audience include graduate students and researchers interested in the methodological aspects of electromagnetic brain imaging.

Autoren/Hrsg.

Sekihara, Kensuke

Nagarajan, Srikatan S.

Inhaltsverzeichnis

1;Contents;7
2;Introduction;12
2.1;1.1 Functional brain mapping;12
2.2;1.2 Electromagnetic brain imaging;13
2.3;1.3 Spatial .lters;14
2.4;1.4 Book chapter organization;16
2.5;1.5 Acknowledgements;18
3;Sensor array outputs and spatial . lters;20
3.1;2.1 Neuromagnetic signals as sensor-array outputs;20
3.1.1;2.1.1 De.nitions;20
3.1.2;2.1.2 Sensor lead field;21
3.1.3;2.1.3 Linear independence of lead-field vectors;22
3.2;2.2 Bioelectromagnetic inverse problem;24
3.3;2.3 Expressions of data covariance matrices;26
3.3.1;2.3.1 Data and source covariance relationship;26
3.3.2;2.3.2 Formulation for uncorrelated sources;28
3.4;2.4 Low-rank signal modeling;29
3.4.1;2.4.1 Definition of noise and signal subspaces;29
3.4.2;2.4.2 Property of the data covariance matrix;30
3.5;2.5 Spatial filters;33
3.5.1;2.5.1 Source reconstruction using a spatial filter;33
3.5.2;2.5.2 Scalar and vector spatial filters;34
3.5.3;2.5.3 Resolution kernel, point-spread function, and beam response;36
4;Tomographic reconstruction and nonadaptive spatial filters;38
4.1;3.1 Minimum-norm method;38
4.1.1;3.1.1 Tomographic reconstruction formulation;38
4.1.2;3.1.2 Nonadaptive spatial-filter formulation;42
4.2;3.2 Variants of the minimum-norm filter;43
4.2.1;3.2.1 Weight-normalized minimum-norm filter;43
4.2.2;3.2.2 sLORETA filter;43
4.3;3.3 Spatial matched filter;45
4.4;3.4 Deriving the minimum-norm-based filters using leakage minimization;46
5;Adaptive spatial filters;48
5.1;4.1 Deriving weights for adaptive spatial filters;48
5.1.1;4.1.1 Minimum-variance spatial filter with the unit-gain constraint;48
5.1.2;4.1.2 Minimum-variance spatial filter with the array-gain constraint;50
5.1.3;4.1.3 Minimum-variance spatial filter with the unit-noisegain constraint;50
5.2;4.2 Prerequisites for the adaptive spatial-filter formulation;51
5.2.1;4.2.1 Uncorrelated source time courses;51
5.2.2;4.2.2 Low-rank signals;54
5.3;4.3 Scalar adaptive spatial filter: deriving the optimum source orientation;55
5.4;4.4 LCMV spatial filter;57
5.5;4.5 Vector adaptive spatial filter formulation;59
5.5.1;4.5.1 Unit-gain constraint spatial filter;59
5.5.2;4.5.2 Array-gain constraint spatial filter;60
5.5.3;4.5.3 Unit-noise-gain constraint spatial filter;62
5.5.4;4.5.4 Equivalence between the adaptive scalar and vector formulations;64
5.6;4.6 Frequency-domain implementation;65
5.7;4.7 Numerical examples;68
6;Location bias, spatial resolution, and beam response;76
6.1;5.1 Bias properties of various spatial filters;76
6.1.1;5.1.1 Definition of source location bias;76
6.1.2;5.1.2 Bias for the spatial matched filter;77
6.1.3;5.1.3 Bias for the minimum-norm filter;78
6.1.4;5.1.4 Bias for the weight-normalized minimum-norm filter;78
6.1.5;5.1.5 Bias for the sLORETA filter;79
6.1.6;5.1.6 Bias for the unit-gain minimum-variance spatial filter;79
6.1.7;5.1.7 Bias for the array-gain minimum-variance spatial filter;80
6.1.8;5.1.8 Bias for the unit-noise-gain minimum-variance spatial filter;80
6.2;5.2 Effects of noise on the location bias;81
6.3;5.3 Spatial resolution;82
6.4;5.4 Spatial-filter beam response;83
6.5;5.5 Numerical examples;85
7;Output SNR and array mismatch;94
7.1;6.1 Output SINR;94
7.2;6.2 Adaptive spatial filters that attain the maximum SINR;96
7.3;6.3 SNR transfer factor;98
7.4;6.4 Two types of SNR de.nitions for the vector minimum- variance spatial filter;100
7.5;6.5 Influence of array mismatch;103
7.6;6.6 Diagonal loading;104
7.7;6.7 Asymmetric diagonal loading;106
7.8;6.8 Eigenspace-projection spatial filter;108
7.8.1;6.8.1 Eigenspace projection;108
7.8.2;6.8.2 Extension to vector spatial-filter formulation;112
7.9;6.9 Numerical examples;114
8;Effects of low-rank interference;120
8.1;7.1 Influence of low-rank interference;120
8.1.1;7.1.1 Low-rank interference;120
8.1.2;7.1.2 Analysis when Rd is a rank-one matrix;122
8.1.3;7.1.3 Analysis when Rd is a rank-two matrix;124
8.2;7.2 Influence on output of the unit-noise-gain minimum- variance filter;125
8.3;7.3 Effects on the output of the eigenspaceprojected spatial filter;126
8.4;7.4 Numerical examples;127
9;Effects of high-rank interference;136
9.1;8.1 Influence of background brain activity;136
9.1.1;8.1.1 Point-spread function under background interference;136
9.1.2;8.1.2 Numerical examples;138
9.2;8.2 Prewhitening eigenspace-projection spatial filter;140
9.2.1;8.2.1 Prewhitening signal covariance estimation;140
9.2.2;8.2.2 Prewhitening eigenspace-projection spatial filter;143
9.3;8.3 Overestimation of signal-subspace dimensionality;144
9.4;8.4 Reconstruction of induced activity;146
9.4.1;8.4.1 General background;146
9.4.2;8.4.2 Prewhitening method;147
9.5;8.5 Numerical examples;149
10;Effects of source correlation;156
10.1;9.1 Performance of adaptive spatial filters in the presence of correlated sources;156
10.2;9.2 Signal cancellation and estimation of source correlation;158
10.3;9.3 Suppression of coherent interferences using the LCMV spatial filter;160
10.3.1;9.3.1 Weight-vector derivation;160
10.3.2;9.3.2 Extension to eigenspace-projected spatial filter;162
10.4;9.4 Imaging magnitude source coherence;163
10.5;9.5 Numerical examples;166
11;Effects of using the sample covariance matrix;174
11.1;10.1 Sample covariance matrix: the maximumlikelihood estimate of the true covariance matrix;174
11.2;10.2 Effects of using sample covariance matrices on the minimum- variance filters;175
11.3;10.3 Recovering from the sample covariance effects: Beamspace processing;177
11.4;10.4 Numerical examples;179
11.4.1;10.4.1 Effects of using sample covariance matrices;179
11.4.2;10.4.2 Recovering from the sample covariance effects;179
11.4.3;10.4.3 Effects of using sample covariance matrices on unit- noise- gain minimum- variance filter;180
12;Statistical evaluation of the spatial filter output;190
12.1;11.1 Problem with Gaussian-distribution-based methods;190
12.2;11.2 Evaluation of statistical significance using nonparametric statistics;191
12.2.1;11.2.1 Voxel-by-voxel statistical significance test;191
12.2.2;11.2.2 Multiple comparisons using maximum statistics;192
12.2.3;11.2.3 Modification for power image;193
12.2.4;11.2.4 Multiple comparisons using the false discovery rate;194
12.3;11.3 Deriving a voxel-wise empirical null distribution;196
12.3.1;11.3.1 Method when the signal is time-locked and the interference is non- time- locked to the stimulus;196
12.3.2;11.3.2 Method when both the signal and the interference are non- time- locked to the stimulus;197
12.4;11.4 Non-parametric method using reconstructed voxel time courses;198
12.5;11.5 Numerical examples;199
13;Methods related to adaptive spatial filters;204
13.1;12.1 Wiener filter;204
13.1.1;12.1.1 Minimum-mean-squared-error criterion;204
13.1.2;12.1.2 Derivation of the minimum-variance spatial filter;206
13.2;12.2 MUSIC algorithm;207
13.2.1;12.2.1 Single- and multi-dipole search;207
13.2.2;12.2.2 Making use of the noise subspace–the MUSIC algorithm;208
13.3;12.3 Scanning with the generalized-likelihoodratio test function;209
13.3.1;12.3.1 Data model;210
13.3.2;12.3.2 Deriving the scanning function;211
13.3.3;12.3.3 Numerical examples;214
14;Appendices;216
14.1;13.1 Maximum-likelihood estimation of noise and signal subspaces;216
14.2;13.2 Additional topics related to non-adaptive spatial filters;218
14.2.1;13.2.1 Determination of the optimum orientation for scalar non- adaptive spatial filters;218
14.2.2;13.2.2 Equivalence between the vector and scalar minimumnorm filters;219
14.3;13.3 Rayleigh-Ritz formula;220
14.4;13.4 Supplementary formulae when only one or two sources exist;222
14.5;13.5 Robustness of the prewhitening signal covariance estimation to the control- only- sources scenario;225
14.6;13.6 Derivation of GLRT scanning function in Eq. ( 12.45);228
14.7;13.7 Bioelectromagnetic forward modeling;231
14.7.1;13.7.1 Quasi-static Maxwell’s equations;232
14.7.2;13.7.2 Magnetic field in an infinite homogeneous conductor;232
14.7.3;13.7.3 Electric potential in an infinite homogeneous conductor;234
14.7.4;13.7.4 Formulae in a bounded conductor with piecewise- constant conductivity;234
14.7.5;13.7.5 Magnetic field from a homogeneous spherical conductor;235
14.7.6;13.7.6 Magnetic field from a realistically-shaped conductor;237
14.7.7;13.7.7 Electric potential for a multiple-shell conductor;242
15;Bibliography;244
16;Index;254